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August 10th, 2016, 07:12 AM   #1
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rate of change/of a line

Hi I'm studying for a calculus test I understand how to get a slope and when a number is beside an x when written as an eqution y = mx + 1 the variable for x will be the slope but in my question the slope is x^2(x squared) which is totally confusing me,can anyone help walk me through how to get the answer

here is the question

If two variables x and y are related by the equation y = 3x^2 – x calculate the average rate of change of y with respect to x as x varies from 3 to 5.

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August 10th, 2016, 07:41 AM   #2
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if $y = f(x) = 3x^2-x$, then the average rate of change of $f(x)$ is $\dfrac{f(5)-f(3)}{5-3}$
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August 10th, 2016, 08:56 AM   #3
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note that the average rate of change is the slope of the $\color{red}{line}$ connecting the two points on the curve ... $(3,f(3))$ and $(5,f(5))$
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August 10th, 2016, 09:08 AM   #4
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thanks for the reply Skeether much appreciated

how come we sub in both 3 and 5 I thought they are both x values?

I thought we could only sub in y and x to the slope formula?

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August 10th, 2016, 09:33 AM   #5
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y is a function of x ... in other words, the value of y depends on the value of x

at $x = 5$, $y = f(5) = 3(5)^2 - 5$

at $x = 3$, $y = f(3) = 3(3)^2 - 3$

slope = $\dfrac{y_2-y_1}{x_2-x_1} = \dfrac{f(5)-f(3)}{5-3}$

Last edited by skeeter; August 10th, 2016 at 09:41 AM.
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